Foundation and Higher · HCF and LCM

HCF and LCM
with prime factors.
Tree, then Venn.

works for any
two numbers

the building blocks of every number —

Prime factors

every whole number is a

product of primes, in one way only

step 1 of 4

Factor tree for 60

1. Split into a factor pair. Circle primes.

2. Keep going until every end is prime.

✓ 60 = 2² × 3 × 5

step 2 of 4

And for 84

1. Same method: 84 = 2 × 42, and so on.

2. Any factor pair gives the same primes.

✓ 84 = 2² × 3 × 7

step 3 of 4

Venn diagram: HCF

1. Shared primes go in the middle: 2, 2, 3.

2. What is left goes outside: 5 and 7.

✓ HCF = the middle: 2 × 2 × 3 = 12

step 4 of 4

Same diagram: LCM

1. Multiply everything in the diagram.

2. 5 × 2 × 2 × 3 × 7, or 5 × 12 × 7.

✓ LCM = 420

HCF and LCM —

Factor trees

write each as a product of primes

HCF

multiply the middle of the Venn

LCM

multiply everything in it

HCF is the smaller answer.
LCM is the bigger one.

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